The value of λ such that sum of the squares of the roots of the quadratic equation, x 2 + 3 - λ x + 2 = λ has the least value is:

Step-by-step solution

We have, x 2 + ( 3 - λ ) x + 2 = λ ,   have roots  α   &   β . Then, f ( λ ) = α 2 + β 2 = α + β 2 - 2 α β = 3 - λ 2 - 2 2 - λ = λ 2 - 6 λ + 9 - 4 + 2 λ = λ 2 - 4 λ + 5 f ′ λ = 2 λ - 4 = 0 for the minimum value of f λ As f '' ( λ ) = 2 > 0 ⇒ λ = 2